Lesson 3- using rules of exponents The exponent, tells the number of times that the base is used as a factor 2 3 is defined as 2 times 2 times 2

Definition of negative exponents  X -n = 1/x n  2 -3 = 1/2 3

simplfy  1/3 -2  3 -3   3 -3  1/5 -2  5 -2   (-5) -2  -(-5) -2

Product rule for exponents  x m x n = x m+n

Power rule for exponents  (x m ) n = x mn

Scientific notation  Multiplying by a positive power of 10, moves the decimal point to the right.  Multiplying by a negative power of 10, moves the decimal point to the left

Simplifying expressions in scientific notation  (4.2 x )(.0028)  2400(1.6 x )  (.0003 x )(4000)  (.006 x )(2000 x 10 4 )

Lesson 6 finding percent of change  Any fraction or decimal can be written as a percent.  To write a decimal as a percent, multiply by 100(move decimal point 2 places to the left)  To write a fraction as a percent, divide the numerator by the denominator, then multiply by 100

examples  Change.12 to a percent  Change 8 to a percent  Change 4/5 to a percent  Change 22/8 to a percent  Change.035 to a percent

Percent of change  Percent of change is the increase or decrease given as a percent of the original amount  When the new amount is greater than the original amount, the change is a percent increase  When the new amount is less then the original amount, the change is a percent decrease

Percent of change  Percent of change= amount of increase or decrease  original amount

practice  Calculate the percent of change and tell whether it is an increase or decrease.  From 120 to 168  From 6 to 5.1  From 18 to 72  From 240 to 60

Determining new amount  What is the new amount when 58 is decreased by 70%?  1. find amount of decrease  70% of 58=.70x58 = 40.6  2. subtract amount of decrease from original amount  = 17.4  OR  1. subtract 70% from 100% = 30%  2. find 30% of 58 = 17.4

What is the new amount when 125 is decreased by 15%  x 125=18.75  =  Or  %- 15%= 85%  2. 85% x 125 =

Find new amount when 620 is increased by 350%.  1. find 350% of 620 = 3.5 x 620 =2170  2.add 2170 to 620= 2790  Or  1. add 100% to 350%= 450%  2. find 450% of 620= 4.5 x 620= 2790

discount  When an item in a store is on sale, the new price reflects a discount.  The amount of discount is the difference between the old and new price and the percent of discount is a percent of discount

 When the price of an item increases, the increase is a markup, and the percent of change is a percent increase.  A markup can refer to an increase in the retail price of an item or it can refer to the amount by which the wholesale cost of the item is increased.  Marked up price=original price +markup  =(wholesale price) + markup  Sale price = original price - discount

Find sale price  A digital camera costs $128. It is being offered at a 25% discount. Find the sale price.  Sale price = original price - discount  S = % x 128  S = = $96  Or  100% -25% = 755  75% of 128 = 96

Finding marked up price  A grocer buys watermelon from a farmer for $1.34 each and sells them at a 250% markup. What is the cost of the watermelon at the grocer's store.  Marked up price= wholesale price+ markup  = % of 1.34  =  = 4.69

Check for understanding  Explain how to find the new amount when a number is increased by a percent.  Explain the difference between a discount and a markup.  A student states that a negative exponent means the exponential must be in the denominator. Is this correct? Explain.